Does Detracking Work? Evidence from a Mathematics Curricular ...

Detracking 3Warning of a “rising tide of mediocrity that threatens our very future” the commission arguedthat all high school students should be required to complete a “New Basics” curriculumincluding 4 years of English, 3 years of mathematics, 3 years of science, and 3 years of socialstudies. Published at a moment in which technological change was boosting the demand forhighly skilled workers (Goldin & Katz 2008), the report hit a nerve. In the years immediatelyfollowing its publication, states enacted an estimated 700 new pieces of educational policy, manyof which raised standards for grade promotion and high school completion (Darling-Hammond& Berry 1988; Timar & Kirp 1989; Wilson & Rossman 1993). By 2008, 25 states requiredstudents to satisfy the “New Basics” academic courses in order to earn a high school diploma(Education Commission of the States 2010) 1 and 24 states had implemented high school exitexams in order to certify that graduates have mastered basic academic skills (Center onEducation Policy 2009).In the decades that followed, secondary schools across the U.S. took large steps towardimplementing the commission’s vision. Between 1982 and 2004, the number of academic coursecredits earned by the average U.S. high school graduate increased by more than 30 percent, from15 to 19. As American high school students complete a greater number of academic courses,they also reach higher levels of coursework. This trend is most discernible in mathematics, wherenearly all high schools send students through a sequence of academic mathematics courses thatbegins with Algebra I. In 1982, more than 20 percent of high school graduates earned theirdiploma without completing a single academic mathematics course and an additional 20 percentof high school graduates finished no mathematics beyond Algebra I. In contrast, just 7 percent of1 The curricular requirements for this count exclude the half year of computer science included in the “New Basics”curricula, since data on state computer science requirements are not widely available.http://mb2.ecs.org/reports/Report.aspx?id=735

Detracking 4graduates in the class of 2004 nationwide finished high school without completing an academicmathematics course and less than 7 percent of 2004 high school graduates finished nomathematics beyond Algebra I. At the same time, the proportion of high school graduates whoearned credit in pre-Calculus or Calculus increased from 10 percent to nearly 35 percent(Authors 2011).California’s Algebra-for-all movementThese shifts are particularly pronounced in California. In 1987, California’s StateSuperintendent of Public Instruction argued that detracking middle schools was a central steptoward raising academic standards in high schools. In 1992, the state department of educationissued curricular standards in mathematics calling for “heterogeneous grouping and detracking asa goal” and the 1997 revision of the state’s content standards called on middle schools to enrollall 8 th graders in Algebra I. The adoption of these standards spurred rapid intensification inmiddle school mathematics curricula in California. Between 1999 and 2008, the proportion ofCalifornia 8 th graders enrolled in algebra more than tripled, from 16 percent to 51 percent (Rosin,Barondess, Leichty 2009). In 2008 the California State Board of Education voted to make theAlgebra California Standards Test (CST) the “sole test of record” for the state’s 8 th graders. Thisrequirement creates strong incentives for California schools to enroll all 8 th graders in Algebra inorder to meet the expectations of No Child Left Behind as well as California state accountabilitypolicy (Rosin, Barondess, Leichty 2009). However, the future of California’s algebra-for-allpush is currently uncertain as the state adopts the national Common Core Standards.In this paper, we evaluate the consequences of curricular intensification in a largeCalifornia public school district. This district, which we pseudonymously refer to as “ToweringPines” was an early mover in the state’s push to enroll more 8 th graders in Algebra. In the 2004-

Detracking 52005 school year, the district offered four main mathematics course options for 8 th graders: Pre-Algebra, Algebra Ia (the first year of a two-year Algebra course sequence), Algebra Ip (a oneyearAlgebra course), and Geometry. Just 32 percent of 2004-2005 8 th graders enrolled in the fullAlgebra I course, and less than 2 percent enrolled in Geometry. In the years that followed, thedistrict phased out the Pre-Algebra course offering, and gradually began placing more and more8 th graders in the 1 year Algebra and Geometry courses, putting more students on track to takeCalculus by graduation. By the 2007-08 school year, more than 70% of the district’s 8 th graderswere enrolled in the one-year Algebra course and an additional 13 percent were enrolled inGeometry.The intensification of 8 th grade mathematics enrollment that occurred between 2004-05and 2007-08 in Towering Pines was a largely exogenous shift and did not correspond withnoticeable changes in the district’s student composition. While Towering Pines isdemographically distinctive, the increase in academic mathematics course enrollments thatoccurred in the district epitomize the curricular changes that have been occurring in Americanmiddle and high schools over the last two decades. By examining changes in course enrollmentpatterns, classroom composition, and student achievement between 2004-05 and 2007-08 inTowering Pines, we seek to shed light on the effects of curricular intensification on: (1) thesocial organization of schools, (2) student exposure to advanced mathematics courses, and (3)the distribution of student achievement. In doing so we address changes in two key elements ofthe tracking system identified by Sorenson (1970): inclusiveness, the extent to which high-levelcoursework is available to students, and selectivity, the extent to which tracking produceshomogeneous learning environments.Constrained curriculum and the effects of curricular intensification

Detracking 6Lee’s notion of “constrained curriculum” (e.g. Lee 1993:140) provides a useful lens forunderstanding curricular intensification, both in Towering Pines middle schools, and throughoutAmerican secondary education. Like students in middle and junior high schools throughout theUnited States, 8 th graders in most California middle schools have the option of enrolling in oneof several tiered mathematics courses, including remedial and applied mathematics, generalmathematics, pre-Algebra, Algebra, and, for a handful of particularly advanced students,Geometry or higher level mathematics. California’s Algebra-for-all 8 th graders policy aims toreplace this differentiated mathematics curriculum with a more constrained curriculum, in which8 th graders can only enroll in Algebra or a more advanced mathematics course. In ToweringPines, this movement took the form of eliminating the bottom rung of the tiered 8 th grademathematics course hierarchy. Lee and her colleagues hypothesize that this move toward a moreconstrained mathematics curriculum will simultaneously raise student achievement and reduceeducational inequalities (Lee and Smith, 1995; Lee, Smith, and Croninger 1997).Lee’s constrained curriculum hypothesis springs directly from the literature on the effectsof curricular tracking. This literature is methodologically diverse, drawing upon nationallyrepresentative data (Argys, Rees, Brewer 1996; Gamoran 1987; Gamoran 1992) as well as casestudies of particular school districts using administrative, survey, and qualitative data (Gamoran,Nystrand, Berends, & LePore 1995; Hallinan, Oakes 2005; Rosenbaum 1976). Despite theirmethodological differences, studies regarding the effects of tracking almost universally indicatethat placement in low-track courses lowers student achievement while placement in higher-trackcourses raises student achievement. As a result, a strong scholarly consensus holds that thepractice of tracking in American secondary education produces inequality without substantiallyimproving educational efficiency. Furthermore several studies indicate that challenging course

Detracking 7placements have positive average effects on student learning and educational attainment(Authors 2008; Chaney, Burgdorf & Atash 1997; Gamoran & Hannigan 2000).However, two empirical challenges make it difficult to rigorously evaluate theconstrained curriculum hypothesis. The first of these challenges is selection bias. In their tests ofthe constrained curriculum hypothesis, Lee and colleagues compare student outcomes betweenschools that enroll all students in college preparatory courses and schools that do not, controllingfor student academic and family background. While potentially informative, this approachassumes that there are no unmeasured differences between these two categories of schools andthe students who choose to enroll in them. This assumption is restrictive and ultimatelyimpossible to empirically assess. In an attempt to address the issue of selection bias, Authors(2008) use propensity score matching to compare students who enroll in academically rigorouscourses with a balanced sample of students who take less rigorous courses. Their findingssuggest that academic course enrollments have positive effects net of selection.However, Authors (2008) are unable to address a second challenge: since policy efforts toenroll all students in college preparatory courses also likely increase student skill heterogeneitywithin these courses, a test of the constrained curriculum must separate the effects of rigorouscurriculum from the effects of sharing a classroom with peers at different achievement levels(Zimmer 2003). This ambiguity has important consequences for the constrained curriculumhypothesis. If peer achievement exerts an independent influence on student learning, policies thatincrease classroom heterogeneity by pushing more students into advanced academic courses maynot be as effective as earlier findings suggest. As most of the students in nationallyrepresentative samples enroll in ability-grouped courses, it is impossible to distinguish between

Detracking 9curriculum designed to prepare them to take Algebra courses in the 8 th grade, the district alsocreated optional “mathematics workshop” courses, in which an average of 8 students met everyother day with their regular mathematics teacher for supplementary help with the acceleratedcurriculum. Burris and colleagues find, in a series of interrupted time-series analyses, that thesereforms increased students’ odds of completing high-level high school mathematics courses, aswell as their odds of earning high-status Regents and International Baccalaureate diplomas. Thisdistrict’s experience suggests that curricular reforms can have positive effects on student coursecompletion, particularly when they are part of a broader effort to improve educational offeringsfor disadvantaged students. However, these analyses are limited in that they provide noinformation regarding the effects of curricular reform on student achievement for their fullsample, although they do find that AP Calculus scores improved among students taking APCalculus exams. Thus, while they show that the reforms are helpful in ameliorating differencesin course-taking, they are unable to examine how this ultimately affects student learning.Evaluations of the Chicago Public Schools’ (CPS) 1997 move to eliminate remedialmathematics coursework and require all students to enroll in college preparatory courseworkyield less encouraging results (Allensworth, Nomi, Montgomery, & Lee 2009). The CPS policywas larger in scale than the Long Island district detracking effort, encompassing all high schoolsin the US’s third largest public school district. However, it was considerably more modest inscope. CPS required all 9 th graders to enroll in Algebra I and college prep English andimplemented an intensive “double-dose” algebra curriculum that enrolled low-achieving studentsin a supplementary Algebra “support” course as well as a mainstream Algebra I course (Nomi &Allensworth 2010). However, CPS did not conceive of this policy as a broad-based detracking.In particular, the district did not intensify its middle school curricula or invest in substantial

Detracking 10teacher professional development to prepare students for the 9 th grade change. As such, the CPSeffort is arguably a purer test of the constrained curriculum hypothesis. Not surprisingly, as inNew York the CPS policy boosted the odds that low-achieving students enrolled in collegepreparatory courses. However, many of the CPS students who enrolled in more rigorous coursesunder the policy failed. Further, Allensworth et al. find no evidence to suggest that the policyimproved average achievement test scores, narrowed test score inequalities, or influenced studenthigh school graduation or college enrollment rates.Understanding failed reformsWhy might some curricular intensification reforms fail to improve student outcomes andnarrow inequalities? One possibility is that curricular reforms fail to fundamentally change thesocial organization of the school. Lucas’s (1999) theory of effectively maintained inequalitysuggests that racial and class-based inequalities in access to rigorous courses will persist evenafter districts move to eliminate lower-track courses and constrain the curricular choicesavailable to students. Rather than undermining ability grouping, Lucas’s theory suggests thatcurricular reforms cause course credit inflation. Such policies may succeed in moving studentsout of remedial courses and into mainstream academic courses. However, if high-status parentsdemand new curricular opportunities to distinguish their children’s educational achievements,class, race, and skills-based inequalities in access to advanced courses may persist. A large bodyof qualitative and case-study educational research conducted in schools, districts and states in theprocess of undertaking broad curricular reforms supports this hypothesis, documenting the arrayof structural and ideological factors that allow high-status parents to “work the system” (Wells &Oakes 1996, p. 137; Yonezawa, Wells & Sarna 2002) and reproduce their social advantages.Furthermore, implementation studies from schools, districts, and states that have undertaken

Detracking 11broad curricular reforms suggests that patterns of social stratification in high school coursetakingpatterns are remarkably robust (Gamoran & Weinstein 1998; Wilson & Rossman 1993).Oakes and colleagues argue that since tracking practices resonate with educators’ theories ofstudent intelligence; teachers and administrators are often reluctant to adopt heterogeneousclassroom organizational schemes (Oakes & Guiton 1995; Oakes, Wells, Datnow, & Jones 1997;see also Sandholtz, Ogawa, & Scribner 2004). If this explanation is correct, curricular reformsmay not serve to actually constrain the curriculum.However, this explanation does not seem to apply to CPS curricular reform, where thepolicies substantially changed the student composition in college preparatory courses(Allensworth et al. 2009). Rather, Allensworth et al. suggest that the policy’s failure was due tothe pedagogical challenges associated with teaching heterogeneous courses. This explanationsuggests that the constrained curriculum hypothesis is mistaken, and ability-grouping haspositive effects for high-achieving and low-achieving students alike. Qualitative evidence fromother detracked schools lends some support to this explanation (Loveless 1999; Rosenbaum1999). For example, based on interviews with teachers in a high school that had undertaken amajor curricular reform, Rosenbaum (1999) argues that teachers in heterogeneous classroomsstruggle to simultaneously engage students of divergent skill levels. Rosenbaum writes (1999, p.2) that: “Increased variation among students made extra attention to the various groups anecessity, but when teachers offered this help to one group, students in the other groups tended tobecome restless and disengaged. Teachers tried to steer a middle ground by teaching to themiddle of the class; but as they did, they were acutely aware of losing students at both extremes.”Alternatively, iatrogenic peer effects may explain disappointing results associated withefforts to intensify curricula and detrack schools. There is strong evidence to suggest that peers

Detracking 12exert a positive effect on student achievement (Hanushek, Kain, Markman, & Rivkin 2003;Hoxby 2000). By design, detracking policies change the peer composition of classrooms. TheCPS algebra-for-all policy, for example, improved peer quality for the low-achieving students itmoved from Pre-Algebra or general mathematics courses to Algebra I. At the same time,however, the policy lowered mean achievement in Algebra classrooms by moving lowperformingstudents from general math courses to Algebra courses. Assuming peer quality has asimilar effect on low- and high-achieving students, the changes in peer quality that low- andhigh-achieving students experience likely cancel one another out and the net peer effectassociated with the CPS Algebra-for-all policy or a similar policy is likely zero. However,Zimmer (2003) argues that peer quality exerts a greater effect on learning for high-achievingstudents than low-achieving students. If this is the case, peer effects may indeed underminedetracking policies like the CPS Algebra-for-all policy.The shape of peer effects may be more complicated in schools that undertake curricularintensification while maintaining a stratified course sequence. Towering Pines, for example,increased the proportion of students in upper-level courses and reduced the proportion ofstudents in lower-level courses, but did not completely eliminate these courses. While lessdramatic than the New York and CPS detracking efforts, this sort of curricular intensification ismore typical of the changes that have occurred in American secondary schools at large over thelast two decades. In this case, curricular intensification may raise peer quality for students whohave been moved to a higher-level course. At the same time, it likely lowers peer quality for lowachievingstudents who remain in low-level courses even as it lowers peer quality for higherachievingstudents who remain in more advanced courses. In this case, the peer effects associated

Detracking 13with detracking may be negligible across an entire population, but noticeable and negative withincourse levels. 2The current studyLike earlier analyses of detracking efforts in New York and Chicago, our analyses takeadvantage of a policy-driven change in school social organization to estimate the effects oftracking net of confounding selection effects. Unlike the broad de-tracking efforts that occurredin New York and Chicago analyses, however, we focus on a curricular intervention thatmaintained a stratified course sequence. As the prior discussion of peer effects makes clear, thisaspect of Towering Pines’ curricular intensification introduces substantial conceptual challenges.However, Towering Pines is not alone in intensifying curricula even while maintaining coursestratification. Indeed, although curricular intensification in Towering Pines has been uniquelyfast-paced; the increase in the proportion of students who take high-level courses and the declinein the proportion of students who take low-level courses in Towering Pines parallel the shifts insecondary school course enrollments that have occurred recently across the U.S. We thus arguethat the changes we observe in Towering Pines provide important insights into the effects ofcurricular intensification. In this paper, we draw upon administrative data on every 8 th grader in2 A thought experiment helps to illustrate the complex relationship between curricular intensification within astratified course sequence and classroom peer composition. Consider a school with 100 students that undertakes apattern of intensification similar to that undertaken in Towering Pines over the study period. Prior to curricularintensification, 75 of the students in this hypothetical school took General Math; 20 took Algebra I; and 5 tookGeometry. After curricular intensification, 25 took General Math; 60 took Algebra I; and 15 took Geometry.Assuming curricular intensification redirects stronger students to higher course levels, the 25 students who tookGeneral Math after curricular intensification in this hypothetical case would have considerably lower quality peersthan they would have without the curricular change. If the school’s course sorting mechanism is meritocratic, the 50students who were redirected from General Math to Algebra I would have higher quality peers than they would havein General Math, but likely only slightly so, curricular intensification has redirected all but the 10 lowest-scoringAlgebra I students to a higher course. Curricular intensification lowers peer quality for the 10 students left inAlgebra I; raises peer quality for the 10 students redirected from Algebra I to Geometry; and lowers peer quality forthe 5 students who remain in Geometry.

Detracking 14Towering Pines in the 2004-2005 through 2007-2008 school years to address three researchquestions:1) What effect did 8 th grade curricular intensification have on mathematics course-takingpatterns in Towering Pines Unified schools?2) What effect did 8 th grade curricular intensification have on classroom-level ethnic,language-based, and skills-based segregation in the district?3) What long-term effects did 8 th grade curricular intensification have on students’mathematics course taking and mathematics achievement?Towering Pines is an immigrant enclave in the inner-ring suburbs of a major metropolitanarea. The district’s student population is ethnically diverse and largely economicallydisadvantaged. More than fifty percent of the students in our sample are Latino, approximately25 percent are Vietnamese, and approximately 15 percent are white. Most of the remainingstudents are Asian and 1 percent of the students in the district are African American. Over 60percent of the students in the district were English-language learners when they enrolled inschool, and while a large proportion of these students had been reclassified as English-proficientby the time they were 8 th graders, more than a third of the sample remained classified as EnglishLanguage Learners (ELLs) in their 8 th grade year. This sample is clearly not representative of 8 thgraders nationwide or statewide. However, the district’s demographic profile provides a uniqueopportunity for understanding the consequences of curricular change on a population that is oftenexcluded from rigorous coursework.To measure students’ 8 th grade mathematics course enrollment, we use information aboutthe California Standards Test (CST) that students took in mathematics in the spring of their 8 th

Detracking 15grade year. 3 As Table 1 reveals, Towering Pines 8 th graders in each of the study years take eitherthe General Mathematics (Pre-algebra), Algebra I, or Geometry CSTs. However, the proportionof students taking each of these course-based exams changed dramatically as the districtintensified 8 th mathematics curricula over the study period. The proportion of 8 th graders enrolledin Algebra I more than doubled between the 2004-2005 and 2007-2008 school years, from 32percent to 71 percent. In the same period, the proportion of 8 th graders enrolled in Geometryincreased from less than 4 percent to 13 percent. The curricular intensification that occurredbetween 2005 and 2008 in Towering Pines was far more pronounced than elsewhere inCalifornia. Statewide, Algebra enrollments grew from 47 percent to 51 percent over the studyperiod (Rosin, Barondess, Leichty 2009) and Geometry enrollments grew from 2.7 percent to 3.6percent[Insert Table 1 about here]The remainder of Table 1 indicates that these changes in 8 th grade mathematics courseenrollment patterns were the result of an exogenous policy shift, rather than a change in thestudent body composition. Students in the five cohorts are remarkably similar on each of thedemographic comparisons, with no statistically significant differences in terms of gendercomposition and only moderate changes in ethnic composition. In addition to comparing studentdemographics across cohorts, this table compares the language status of students in the four 8 thgrade cohorts. For the purposes of this paper, students are sorted into three language statuscategories: ELLs are students who entered the district with limited English language skills and3 While we also have access to 8 th grade course titles, these change over the study period, are not entirely consistentfrom school to school, and are often not representative of course content. We choose to instead use the CST thatstudents took, as this better indicates the content covered in the course. Thus, for example, despite the difference incourse titles, students enrolled in “Pre-Algebra” and “Algebra Ia” classes in 8 th grade both finish Algebra I in 9 thgrade, putting them on a track that will not take calculus before graduation. However, both take the General Math(Pre-Algebra) CST, rather than the Algebra I CST, which more accurately captures the fact that they will not havecovered the material in Algebra I by the end of 8 th grade.

Detracking 16have not demonstrated English-language proficiency by their 8 th grade year; Reclassified FluentEnglish Proficient describes students who had limited English skills when they entered thedistrict but who demonstrated proficiency before 8 th grade; all other students, including nativeEnglish speakers and students who were bilingual in English and another language upon districtentry, are in the third category. The language status composition of the district remains relativelystable across the study period. 4 Given this degree of between-cohort balance, we regard thedistrict’s effort to intensify 8 th grade mathematics curricula as a powerful case study forunderstanding the implications of curricular intensification.That said, we note that 8 th grade curricular intensification is not the only change thatoccurred in the district over the study period. In particular, we find that student achievement asmeasured by student scores on CSTs in mathematics and English-language arts administered toall students in the spring of their 7 th grade year improved significantly over the study period.seems unlikely that changes in 8 th grade mathematics placements could drive improvements in7 th graders’ test scores. Furthermore, these trends are roughly consistent with statewide trends in7 th grade student achievement over the study period. We thus view 7 th grade test scores asendogenous and our multivariate analyses control for students’ prior mathematics and Englishscores.MethodsQ1: Estimating changes in course enrollments5It4 It is worth noting that although the level of initially fluent students remains constant, there are some changes in theproportion of those reclassified as proficient. There is some evidence that this is due to the fact that detracking themath classes raised English scores and led some students to be reclassified because it changed the English classes inthese which students were enrolled.5 While the mathematics CSTs administered to 8 th -12 th graders are course-specific; all 7 th graders take the samegrade-specific mathematics CST.

Detracking 17We begin by examining the effects of curricular intensification on 8 th grade courseenrollment patterns in Towering Pines. To address this we estimate a series of generalizedordered logistic regression models on 8 th graders’ odds of enrolling in Algebra or Geometry(Williams 2006). These models can be simplified as:P(Y i >j) = Logit(β 0 + Σ β 1 Year 8 th + Σ β 2 Controls), j=1, 2where Yi is an 8 th grader’s course enrollment odds of enrolling in a course higher than GeneralMathematics (j=1) or Algebra (j=2); Year 8 th is a matrix of dummy variables the school year inwhich the student enrolled in 8 th grade (the 2004-2005 cohort is the reference); and Controlsinclude student gender, ethnicity, language status, and 7 th grade mathematics and EnglishLanguage Arts (ELA) test scores. β 1 in this model, therefore, represents the extent to which 8 thgrade mathematics course enrollments changed over the study period, net of other changes in thedistrict. In an additional model, we add a series of interactions between the Year dummies andthe 7 th grade score variables, in order to estimate the extent to which curricular intensificationchanged the relationships between prior achievement and 8 th grade mathematics courseplacement.Even if Towering Pines’ curricular reforms succeeded in channeling students into moreadvanced courses, their consequences would have been short lived if they did not preparestudents to succeed in these courses and continue to enroll in advanced courses as theyprogressed through school. We thus estimate the effects of Towering Pines’ curricularintensification on student mathematics course enrollments in 10 th grade. 6Using generalized6 We also estimate models examining whether the odds of failing algebra and geometry increased across cohorts, asNomi and Allensworth (2010) show that curricular intensification increased the odds of failure in Chicago. Ourfindings, which we do not report here but are available by request, similarly indicate that suggest that curricularintensification Towering Pines increased student odds of failing a math course between 8 th and 10 th grade,particularly for students who took Algebra in the 8 th grade.

Detracking 18ordered logistic regression models, we estimate cross-cohort changes in 10 th grade mathematicscourse enrollment net of 7 th grade test scores and demographics. These models follow the samegeneral form as the 8 th grade mathematics course enrollment generalized ordered logistic modelssummarized above. As in the 8 th grade course enrollment models, we use students’ coursespecificCST mathematics test to measure their 10 th grade course enrollment. The categories for10 th grade course enrollment are: Algebra I, Geometry, Algebra II, and Summative Mathematics(which is the CST designed for students enrolled in Trigonometry, pre-Calculus, Calculus, or amore advanced mathematics course.)Q2: Estimating changes in classroom compositionSecond, we examine trends in classroom-level gender, ethnic, language-based, and skillsbasedsegregation in the district. This analysis provides a far more detailed picture of the socialsorting that occurs in middle schools than is available elsewhere in the literature. Since we havedata on the specific class that the students were in (e.g. 4 th period algebra with Ms. Smith), wecan examine not only 8 th graders’ rates of enrollment in Algebra and Geometry, but also theextent to which 8 th graders are sorted into different classrooms based on ascriptivecharacteristics, language skills, and past academic performance.We calculate Duncan and Duncan’s (1955) index of dissimilarity (D) to measure thedegree to which students are segregated into different 8 th grade mathematics classrooms based ontheir gender, ethnicity, English language ability, and measured 7 th grade skills. The index ofdissimilarity ranges from 0 to 1, and measures the proportion of members of a given group thatwould have to move to a different classroom to achieve an even distribution across allclassrooms. For example, the index of dissimilarity between ELLs and native English speakerscalculated for all of the classrooms in the Towering Pines district represents the proportion of

Detracking 19ELLs who would have to relocate to another classroom in order to spread all ELLs equallyacross the district. More formally, this measure is defined as:D xy = .5 * Σ | (x i /X) - (y i /Y) |where, for example, x i is the number of ELLs in classroom i and X is the number of ELLsdistrict-wide; y i is the number of native English speakers in the classroom and Y is the number ofnative English speakers district-wide. By comparing dissimilarity measures across the years inwhich Towering Pines intensified 8 th grade mathematics curricula, we capture the consequencesof this curricular reform class-room-level segregation.In addition to examining measures of segregation, we also address changes in classroomcomposition by examining how mean classroom skill level and within-classroom skillheterogeneity students are exposed to changes across cohorts. We calculate mean classroom skilllevel by averaging 7 th grade mathematics achievement scores (measured as a percentile score ofall students across cohorts) for all students in each 8 th grade mathematics classroom in thedistrict. We calculate within-classroom skill heterogeneity by taking the interquartile range of 7 thgrade mathematics achievement (also measured as a percentile score) for each 8 th grademathematics classroom in the district. We report the mean classroom skill level and interquartilerange separately for students in General Mathematics, Algebra I, and Geometry courses in eachcohort.Q3: Estimating changes in the distribution of student test scoresFinally, we estimate the effects of curricular intensification in Towering Pines onstudents’ mathematics skills as measured by the mathematics portion of California’s high-stakeshigh school exit exam (CAHSEE). This exam, which is designed to test student mastery of basicmathematics skills, is administered to all students in the spring of their 10 th grade year. This test

Detracking 20provides a better metric for measuring the consequences of curricular intensification on studentachievement than the mathematics CSTs administered to California high school students, sinceall students take the test in the same form, regardless of their mathematics course enrollment.However, since the most advanced concepts tested on the exit exam are covered in Algebra Icourses, analyses of student scores on the exit exam may understate the effects of curricularintensification. 7 This is particularly true at the top of the skill distribution, where test ceilingeffects make it difficult to assess the extent to which curricular changes influence studentachievement.We first estimate the average effect of curricular intensification on average studentachievement using OLS regression models that take the same general form as the ordered logisticregression models described above. The Year coefficients in these models capture the meanchanges in student mathematics achievement across cohorts, controlling for changes in studentcomposition and 7 th grade skills. In addition, we estimate Year*Course interaction effects tomeasure the extent to which curricular intensification changed the payoff associated with takingAlgebra or Geometry over time. Finally, we add controls for skill heterogeneity and mean skilllevel in 8 th grade mathematics classrooms to determine the extent to which the challengesassociated with teaching heterogeneous classrooms and peer effects mediate the effects ofcurricular intensification on student achievement.We also estimate quantile regression models, which allow us to compare the achievementdistributions of the cohorts at a variety of points in the distribution. For example, while the OLSresults provide us with information about how the mean of two cohorts differ, quantile regression7 We also conduct analyses separately for CAHSEE subscores measuring Algebra I, Algebra and Functions, andMeasurement and Geometry. As there are no noteworthy differences, we do not report them here.

Detracking 21models can provide us with information about how the 10 th , 90 th or any other percentile differsbetween two cohorts. As laid out in Koenker and Bassett (1978), the standard modely=iX kiβ + εkiwhere y i is the mathematics score for student i, and the X k are the independent variables, can beestimated at the θ th quantile by minimizing:min ⎡( ){ }{ } ⎥ ⎥ ⎤⎢ ∑θyi− Xiβ+ ∑ 1−θyi− Xiββ ⎢⎣i yi≥ X iβi yi< X iβ⎦(2)Intuitively, this estimates β k at different quantiles by changing the weights (θ and 1-θ) on thepositive and negative residuals. For example, at the median (θ = .5) positive and negativeresiduals are given equal weight so that the sum of absolute deviations is minimized, while at the90 th percentile (θ = .9) negative residuals are multiplied by .9 and positive residuals aremultiplied by .1, so that the negative residuals have more weight. 8ResultsOur first research question asks about the extent to which curricular intensificationinfluenced mathematics course placements in Towering Pines. Table 2 uses general orderedlogistic regression to model changes in the 8 th grade mathematics course placement regime inTowering Pines between the 2004-2005 and 2007-2008 school years. These analyses make itpossible to examine differences in course taking by cohort while controlling for demographiccharacteristics and 7 th grade test scores. Consistent with the descriptive enrollment statistics8 For an excellent nontechnical introduction to quantile regression, see Koenker and Hallock (2001).

Detracking 22reported in Table 1, we find that 8 th graders’ odds of enrolling in Algebra and Geometry risedramatically over the study period. For example, the odds that 2007-2008 8 th graders enroll inAlgebra or higher (as opposed to General Mathematics) are 9 times higher than the odds of 2004-2005 8 th graders enrolling in Algebra or higher. Similarly, the odds that 2007-2008 8 th gradersenroll in Geometry (as opposed to Algebra or General Mathematics) are 3 times higher than theodds for 2004-2005 8 th graders.[Insert Table 2 about here]This curricular intensification is not an artifact of demographic change in the district or adownstream effect of improvements in elementary mathematics education. Indeed, Model 2 ofTable 2 reveals that the expansion of student advanced mathematics course-taking odds is evenmore pronounced after controlling for student demographic and 7 th grade mathematics test scoresthan it is in the baseline Model 1.In addition to boosting student access to advanced mathematics courses, Towering Pines’curricular intensification push may have influenced the degree to which prior achievementaffects course placement. We see in Model 3 that the role of 7 th grade scores in predicting 8 thgrade mathematics course lessens over the course of the study period. This is noteworthy giventhe importance of cumulative advantage processes in education (Diprete and Eirich 2006, Farkas2003), as it suggests that curricular intensification in Towering Pines weakened one mechanismthrough which skills inequalities widen over students’ educational careers. That is, to the degreethat a deficit in 7 th grade achievement precludes students from taking higher level mathematicsachievement in 8 th grade, these initial deficits are likely to be reinforced and become difficult toovercome. Thus, finding that 7 th grade scores are less predictive of 8 th grade course placementindicates that curricular intensification weakens the link between earlier achievement and later

Detracking 23course taking. The findings present in Table 2 thus show not only that curricular intensificationhas increased the accessibility of Algebra and Geometry in Towering Pines, but it has alsochanged more fundamentally the way course placements are made in the district.The results reported in Table 3 indicate that 8 th grade curricular intensification continuesto influence students’ mathematics course patterns two years later, when students are in 10 thgrade. 10 th graders in the later cohorts are significantly more likely to be enrolled in advancedmathematics courses than students in the first cohort. The odds that students who were in the 8 thgrade in 2007-2008 enroll in Geometry or a higher mathematics course by their 10 th grade year isfour times higher than the odds for students in the 2004-2005 8 th grade cohort. Students in thiscohort were also significantly more likely to enroll in Algebra II or a higher-level mathematicscourse in their 10 th grade year than their peers in the 2003-2004 8 th grade cohort. As in Table 2,these cohort effects remain significant after controlling for cross-cohort changes in studentlanguage status and demographics and 7 th grade mathematics and ELA test scores in Model 2.The expansion of advanced 10 th grade mathematics course enrollments revealed in Table 3 issomewhat less pronounced than the expansion of 8 th grade mathematics course enrollmentsreported in Table 2, indicating that not all students who enroll in more advanced 8 th gradecourses continue to take advanced mathematics courses in 10 th grade. Overall, however, theTable 3 suggests that 8 th grade mathematics curricular intensification has lasting positiveconsequences for student access to advanced mathematics courses, particularly for students withlow 7 th grade mathematics achievement.[Insert Table 3 about here]Table 4 considers the effects of these shifts on gender, ethnic, language-based, and skillsbasedsegregation in the districts’ 8 th grade mathematics classrooms. These findings provide a

Detracking 24look at the extent of classroom-level tracking that is generally unavailable elsewhere in theliterature, since few studies have access to census data and classroom indicators. We find onlymodest change in the extent of gender, ethnic, or language-based segregation in the district’s 8 thgrade mathematics classrooms. However, this table indicates that the district underwent someskills-based desegregation after it implemented its 8 th grade curricular intensification policy. In2004-2005, 68 percent of students who scored in the bottom half on the state’s 7 th grademathematics test would have had to move to another classroom to establish an even distributionof high- and low-skill students in the district. In 2007-2008, by contrast, 52 percent of suchstudents would have had to move to a new classroom. We find similar evidence of skills-baseddesegregation when we consider the extent to which students that scored in bottom quartile onCalifornia’s 7 th grade mathematics test, which roughly corresponds to the students who arecategorized as below basic proficiency in 7 th grade mathematics, shared 8 th grade mathematicsclassrooms with students who scored in the top quartile of the 7 th grade test. Furthermore,although the changes are less pronounced, we also find evidence to suggest that mathematicsclass segregation based on 7 th grade ELA test scores also declined in the district over the studyperiod.[Insert Table 4 about here]Table 5 provides another look at the way curricular intensification changed thecomposition of 8 th grade mathematics classrooms in Towering Pines. The first panel in this tablereports changes in the mean classroom 7 th grade percentile scores by 8 th grade mathematicscourse (General Mathematics, Algebra, and Geometry) across the study period. Even as 7 th gradetest scores improved for Towering Pines students over the study period, the mean studentachievement level within 8 th grade mathematics class levels declined since the district’s

Detracking 25curricular intensification redirected relatively low-achieving students into higher-levelmathematics courses. In 2004-2005, the average General Mathematics 8 th grade student cameinto the course with a score at the 32 nd percentile on the 7 th grade mathematics assessment ofmathematics achievement. As General Mathematics enrollments declined, so did the incomingscores of General Mathematics students. By 2007-08, the mean 7 th grade mathematics test scorefor 8 th grade students in General Mathematics was at the 20 th percentile. The trend for 8 th gradersenrolled in Algebra and Geometry is similar. Consistent with the ordered logistic regressionsreported in Table 2, these findings indicate that curricular intensification led students with lowerskills levels to be placed in higher-level courses.[Insert Table 5 about here]The second panel in Table 5 considers changes in the concentration of low-performingstudents in Towering Pines math classrooms, measured as the proportion of students who scoredbelow basic on the 7 th grade math California Standards Test. Throughout the study period, alarge proportion the district’s students entered 8 th grade with below basic math scores. While thisproportion fell somewhat as average 7 th grade math scores rose, in 2007-08, 21 percent of thedistrict’s 8 th graders had low incoming math scores. Not surprisingly, these low-performingstudents were largely concentrated in General Math courses. As the district undertook curricularintensification and General Math enrollments shrunk, the concentration of low-performingstudents in General Math increased, from 42 percent to 67 percent. However, many lowperformingstudents also took part in the curricular intensification, and the proportion of Algebrastudents with below basic 7 th grade math skills increased from 1 percent in 2004-2005 to 15percent in 2007-2008.

Detracking 26The third panel of Table 5 reports changes in within-8 th grade classroom interquartileranges on 7 th grade test scores over the study period. These interquartile ranges, which aredefined as the difference between the 7 th grade test score of a student at the 75 th percentile in agiven classroom and the 7 th grade test score of a student at the 25 th percentile, provide a measureof the extent of skill heterogeneity in the students’ 8 th grade mathematics classrooms. 9 We findthat the amount of skill heterogeneity that occurs among peers in General Mathematicsclassrooms declined modestly over the study period. On the other hand, as Algebra andGeometry enrollments expanded, the skill heterogeneity that students in these high-levelclassrooms encountered grew dramatically. This change was particularly pronounced inGeometry classrooms. The average 7 th grade mathematics test interquartile range for 8 th gradersin Geometry classes increased by more than three times between the 2004-2005 and 2007-2008school years. This finding, which is consistent with the finding that curricular intensificationloosened the association between 7 th grade mathematics scores and 8 th grade mathematics courseplacements, suggests that 8 th graders in Geometry classes were exposed to a far wider range ofpeers in the later cohorts than in the earlier cohorts. Taken together, therefore, the analysespresented in Tables 2, 3, 4, and 5 indicate that the Towering Pines’ push to intensify 8 th gradecurricula had lasting effects on students’ math course attainment and the social organization of8 th grade mathematics classrooms.9 The size of the interquartile range for students at a given course level is a function of the proportion of studentsenrolled in a given course, as well as the extent to which students are sorted. A couple of hypothetical examples helpto interpret these values. Take a case where 7th grade skill levels do not vary across cohort, students are sorted intocourses so that there are one-third each in General Mathematics, Algebra, and Geometry, and students are randomlyassigned to classrooms within courses. If course level assignments were entirely random, the interquartile range forskills in General Mathematics, Algebra, and Geometry would equal 50; the interquartile range for the population atlarge. By contrast, if students were perfectly sorted based on 7th grade score, the IQR would equal approximately16.7 (33.3/2). If instead we had 50 percent of students in General Mathematics, and 25 percent each in Algebra andGeometry, then perfect sorting would give us IQR’s of 25 for General Mathematics and 12.5 for Algebra andGeometry, while random sorting would still give IQR’s of 50.

Detracking 27In Table 6 we explore the effects of curricular intensification on mathematicsachievement tests scores by examining student scores on the California High School Exit Examadministered in the spring of students’ 10 th grade year. Model 1 reveals that Towering Pinesstudents who were 8 th graders in 2005-2006, 2006-2007, and 2007-2008 did not scoresignificantly differently on the 10 th grade test than their peers who were 8 th graders in 2004-2005.[Insert Table 6 about here]However, we find in Model 2 that students in the 2005-2006, 2006-2007 and 2007-20088 th grade cohorts scored significantly worse on the high school exit exam than students withsimilar 7 th grade test scores in the 2004-2005 8 th grade cohort. This finding suggests that exitexam gains experienced by Towering Pines students in the later cohorts were the result ofimprovements that occurred prior to their 8 th grade year, where the curricular reform wastargeted. Despite significantly improving students’ odds of enrolling in advanced 8 th and 10 thgrade mathematics courses, curricular intensification failed to boost student mathematicslearning. Indeed, the cohort effects in Model 2 of Table 6 indicates that this policy shift mayhave impeded student learning in mathematics.Why might a policy that increases the rigor of 8 th graders’ mathematics courseplacements have negative long-term effects on their mathematics learning? The remainingmodels in Table 6 test likely explanations for this unexpected negative effect. Model 3, whichincludes a set of mathematics course by cohort interactions, investigates the possibility thatcurricular intensification in Towering Pines could have diluted the effectiveness of Algebra andGeometry courses. The results of this model suggest that the score gains associated with takingdifferent courses changed as curricular intensification came into effect. We see some evidenceto suggest that the difference between General Mathematics and Algebra takers shrank somewhat

Detracking 28over the study period. In the baseline cohort, Algebra takers scored roughly a third of a standarddeviation above the General Mathematics students. In the 2006-2007 cohort, however, Algebratakers scored less than a fifth of a standard deviation better than students in GeneralMathematics. While the interactions for the 2005-2006 and 2007-2008 cohorts are notsignificant, they are both negative. By contrast, the benefits associated with Geometry grew overthe study period. For 8 th graders in the 2004-2005 cohort, enrolling in Geometry had no effect onstudent 10 th grade mathematics achievement net of incoming scores. But by 2007-2008,Geometry course-taking raised student scores by more than half a standard deviation. Thesefindings suggest that while the educational benefits available to Towering Pines students whoenrolled in Algebra courses diminished, the educational benefits available to students whoenrolled in Geometry increased.One way that curricular intensification could hurt student learning in 8 th grade Algebraclassrooms is by increasing the degree of student skill heterogeneity in these classrooms, forcingteachers to attempt to simultaneously meet the needs of an increasingly diverse pool of learners(Rosenbaum 1999). Model 4 of Table 6 considers this possibility by adding a control for skillheterogeneity in 8 th grade mathematics classrooms, measured as the inter-quartile range ofstudents’ 7 th grade mathematics test score. Surprisingly, this analysis indicates that that skillheterogeneity improves student learning, all else equal. Furthermore, controlling for skillheterogeneity does very little to moderate the differential returns associated with higher-levelmathematics course enrollment in 8 th grade. This analysis, therefore, provides little support forthe idea that the skill heterogeneity undermines the effectiveness of curricular reforms thatdetrack by intensifying curricula.

Detracking 29Another possible explanation revolves around changes to peer quality in 8 th grademathematics courses. Model 5 of Table 6 tests this possibility by controlling for peer quality in8 th grade mathematics classrooms via a standardized measure of the mean 7 th grade mathematicstest score for 8 th graders mathematics class peers. Comparing the cohort coefficients in Model 5with the cohort coefficients in Model 3 reveals that peer quality explains approximately a third ofthe decline in student achievement in 8 th grade General Mathematics classrooms that occurred inTowering Pines during the study period. Comparing the Model 3 and Model 5 Algebracoefficients suggests that peer effects explain approximately two-thirds of the advantageassociated with enrolling in Algebra in the baseline year. Likewise, comparing the Model 3 andModel 5 Geometry coefficients suggests that if not for positive peer effects, students in thebaseline cohort would have been better off enrolling in a lower level mathematics course. Whilepeer quality explains some of the apparent decline in the value of Algebra course enrollmentsthat occurred over the study period, the reverse is true for Geometry, where cross-cohortincreases in the returns to enrollment are even stronger after controlling for peer quality. Thus,much of the decline among students in General Mathematics can be attributed to peer effects, ascan much of the base effect of Algebra and some of the changes in the returns to Algebra andGeometry over time.We also introduce peer effects into the model by controlling for the percent of students ineach mathematics course who scored below basic on their 7 th grade mathematics test. Thisapproach allows us to examine a different aspect of peer effects—instead of conceptualizing theeffects of peers as operating through the average level of preparation in a classroom, it suggeststhat the effects of peers operates through the proportion of students who are not well prepared.The results for General Mathematics in Model 6 show that the percentage of the class that is

Detracking 30below basic in 7 th grade mathematics score accounts for much of the decline in learning that weobserve in Model 3, and that this conceptualization of peer effects is slightly better at explainingthis decline than the average classroom achievement (Model 5). Similarly, controlling for lowperformingpeers mediates the relationship between Geometry enrollment and student success inthe study’s later years, suggesting that one of the reasons that enrolling in Geometry improvesstudent achievement is that it protects students from low-performing peers. The pattern forAlgebra is somewhat different. Controlling for low-performing peers explains approximatelyone-third of the baseline Algebra effect. However, the growing proportion of low-achievingstudents enrolled in Algebra courses does not explain the declining returns to Algebra enrollmentthat we observe over the study period.These analyses suggest that iatrogenic peer effects partially explain the disappointingstudent achievement trends that occurred in Towering Pines during the period of curricularintensification. While both measures of peer effects return complementary findings, it isinteresting to note that the classroom concentration of low-performing peers is a somewhatstronger predictor of student achievement than classroom average student achievement levels.Furthermore, we find that the classroom concentration of low-performing peers is a particularlysalient mediator of the negative relationship between low-level math course placement andachievement in the district.Finally, given that many proponents of tracking argue that detracking harms highachieving students, we examine the distributional consequences of curricular intensification inTowering Pines. While Table 6 provides an indication of how successive cohorts differed onaverage from the baseline cohort, Figure 1 examines how the 10 th through 90 th percentilemathematics scores varied across cohorts. Figure 1 reports the results from quantile regression

Detracking 31models estimating Model 2 of Table 6 at different points across the distribution; the y-axisreports the estimate of beta, while the x-axis reports the percentile that we are examining. We seethat for all the 2005-2006 and 2007-2008 cohorts the top of the distribution is close zero, while atthe middle and bottom of the distribution the difference is slightly negative. This indicates thatin these cohorts scores at the top of the distribution are not lowered by detracking, while at thebottom of the distribution scores are not improved, and are in fact lowered. For the 2006-2007cohort, however, we find a slightly different pattern: scores are lower than the 2004-2005 cohortthroughout the distribution, but particularly so at the top end of the distribution. As this is theyear with the largest shift in course enrollments, this suggests that there is a temporarydisadvantage experienced at the top of the distribution but that this effect is not lasting. Thus, wefind no evidence to suggest that detracking 8 th grade mathematics courses in Towering Pines hasdeleterious long term effects on high-achieving students’ learning. Unfortunately, however, wealso find little evidence to suggest that detracking leads to learning gains for low-achievingstudents.[Insert Figure 1 about here]DiscussionDriven by a statewide push to enroll all California 8 th graders in Algebra courses,Towering Pines has dramatically intensified 8 th grade mathematics curricula. Between the 2004-2005 and 2007-2008 school years, the proportion of the district’s 8 th graders who enrolled inAlgebra more than doubled and the proportion of 8 th graders who enrolled in Geometry increasedmore than eightfold. Although remarkable in magnitude and speed, the shifts in 8 th grade courseenrollments that occurred in Towering Pines over this time period are consistent with a broadernationwide trend toward curricular intensification in secondary education. In this paper, we use

Detracking 32Towering Pines’ experience with curricular intensification in middle school mathematics as acase study to understand the implications of curricular intensification more broadly.Specifically, we address three questions: 1) Did the 8 th grade Algebra for all policysucceed in placing more students into higher level mathematics courses; 2) How did the reformsaffect the social organization of schools; and 3) What effects did the policy have on students’mathematics achievement?We find that the push to place 8 th graders into Algebra had lasting impacts on students’course-taking trajectories, raising the odds that Towering Pine students enrolled in academicmath courses in both 8 th and 10 th grades. Thus, we conclude that the policy was successful in itsstated goal. Further, the policy diluted the effect of previous achievement on course placement,so that 7 th grade mathematics achievement is less predictive of 8 th and 10 th grade course-taking inlater cohorts.Decoupling prior achievement from course placement resulted in a substantial decline inclassroom level mathematics skill based segregation. We also find that skill heterogeneityincreased in the district’s Algebra and Geometry classrooms. Together with the declines that weobserve in the average skill level of peers at all three course levels, this suggests that curricularintensification made Algebra and Geometry classes grow less select and thus more variable.Thus, in answer to our second question, we conclude that curricular intensification partiallydetracked mathematics education in the district.Finally, we examine the impact of curricular intensification on mathematics achievement.We find that students at the top of the distribution do not appear to experience long term declinesin scores, though it is possible that large changes in course enrollments might have led to a onetime drop in scores at the top of the distribution. Thus, detractors’ claims that detracking will

Detracking 33harm those at the top of the distribution appear unfounded. Unfortunately, however, we find thatstudents at the bottom of the distribution were negatively affected by the curricularintensification. Given that high achieving students are performing no better, and low achievingstudents are performing somewhat worse, on average curricular intensification negatively affectsstudents’ learning. We examine two explanations for this decline--the pedagogical challengesassociated with teaching a heterogeneous classroom and the effects of being in a classroom withlower achieving peers. We find little evidence that classroom heterogeneity accounts for thechanges that we observe, but peer effects appear to account for a substantial portion of thesechanges. As Algebra courses became modal in the district, the average level of peer achievementin Algebra courses declined. This decline explains a large portion of the fall-off in learning thatoccurred in Towering Pines Algebra classrooms over the study period. At the same time, themovement of relatively high-achieving students into Algebra classes increased the concentrationof low-achieving peers in General Math classes. This concentration explains a large proportionof the decline in learning that occurred in the district’s General Math courses.Similar iatrogenic peer effects may help to explain why the effects of curricularintensification efforts in Towering Pines and the Chicago Public Schools differ so dramaticallyfrom the predicted consequences of a constrained curriculum and the measured effects ofdetracking efforts in Scotland and Long Island. Curricular intensification lowered averagestudent achievement levels in courses across the Towering Pines even as it maintained theconcentration of students with below-basic skills in General Math courses. Similarly, Chicago’sAlgebra-for-all effort integrated 9 th grade mathematics classrooms even as it instituted thedouble-dose Algebra classes that concentrated low-performing students for part of the day. Thesepolicies were designed to detrack mathematics instruction, and for much of the student

Detracking 34population they did. However, these policies also unintentionally reinforced the academicisolation of a relatively small number of low-achieving students.It is possible, therefore, that policies that more fully eliminate instructional tracks, such asthe Long Island policy, may be more efficient and more equitable than policies that attempt tomake access to high-level courses within stratified course sequences more inclusive. However,our analysis suggests that the wholesale detracking strategy pursued in Long Island may alsopose risks. While curricular intensification in Towering Pines did not have a negative effect onachievement for students at the top of the skills distribution, this is largely due to the fact that thedistrict maintained a fairly selective 8 th grade Geometry classes for high-achieving students.While average incoming test scores for 8 th graders in Geometry declined over the study period asGeometry enrollments increased, very few students who had scored below basic in 7 th grademath enrolled in Geometry. This exclusionary policy seems to have boosted the returns toGeometry coursework in the district, and a more broad-based detracking policy might reversethose gains.Another approach that Towering Pines and other districts that undertake curricularintensification might pursue in order to avoid the negative peer effects that we observed is tofocus on improving incoming students’ skill readiness, particularly at the bottom of the skilldistribution. While Towering Pines raised the 7 th grade achievement scores of successive cohortsof students in preparation for taking more advanced 8 th grade mathematics courses, theproportion of students who scored below basic in 7 th grade remained relatively constant. Thesestudents’ early deficits likely constrained their ability to take advantage of the opportunity toenroll in more advanced coursework. Furthermore, our analyses suggest that the concentration oflow-achieving students in math classrooms hurt their classroom peers’ performance. By thinking

Detracking 35about the readiness of the whole classroom and improving skills at the bottom of the distribution,Towering Pines might have avoided these negative peer effects and raised the overalleffectiveness of its 8 th grade algebra-for-all effort.However, peer effects do not fully account for the changes in test scores that we observe.It is therefore worth considering other factors that may explain the disappointing consequencesof curricular intensification for student achievement in Towering Pines. One potential candidateis students’ academic motivation. Our analyses of supplemental motivational data from twocohorts of Towering Pines 8 th graders indicate that curricular intensification lowers studentacademic motivation and efficacy when it causes students to be placed in courses that are abovetheir skill level (Authors 2011b). Another potential candidate is teacher quality. Just ascurricular intensification requires students to take more rigorous courses than they mightotherwise have, it also requires teachers to teach more rigorous courses than they mightotherwise have. If this process creates a mismatch between teacher preference or ability and theircourse assignment, it may undermine teacher effectiveness.In sum, our findings suggest that enrolling students in more rigorous courses is not, initself, enough to raise student achievement. Rather, our analyses suggest that successfulcurricular reforms must prepare students across the skill distribution and carefully attend toclassroom peer dynamics.

Detracking 36ReferencesAuthors. 2008.Authors. 2010.Authors. 2011a.Authors. 2011b.Achieve, Inc. 2010. Closing the Expectations Gap.http://www.achieve.org/ClosingtheExpectationsGap2010Allensworth, Elaine, Takako Nomi, Nicholas Montgomery, and Valerie E. Lee. 2009. CollegePreparatory Curriculum for All: Academic Consequences of Requiring Algebra andEnglish I for Ninth Graders in Chicago. Educational Evaluation and Policy Analysis, 31,367-391.American Diploma Project. (2004). Ready or Not: Creating a High School Diploma ThatCounts. http://www.achieve.org/ReadyorNotArgys, Laura M., Daniel I. Rees, Dominic J. Brewer. (1996). Detracking America's schools:Equity at zero cost? Journal of Policy Analysis and Management, 15, 623–645.Burris, C.B., Heubert, J.P, & Levin, H.M. (2006). Accelerating mathematics achievement usingHeterogeneous Grouping. American Educational Research Journal, 43(1), 137-154Burris, C.C., Wiley, E., Welner, K.G., & Murphy, J. (2008). Accountability, rigor, anddetracking: Achievement effects of embracing a challenging curriculum as a universalgood for all students. Teachers College Record, 110(3), 571-607Chaney, B., Burgdorf, K., & Atash, N. (1997). Influencing achievement through high schoolgraduation requirements. Educational Evaluation and Policy Analysis, 19(3), 229-244.Conger, Dylan, Mark C. Long, and Patrice Iatarola. (2009). Explaining race, poverty, and genderdisparities in advanced course-taking. Journal of Policy Analysis and Management, 28,555–576.Dalton, B., Ingels, S.J., Downing, J., Bozick, R., & Owings, J. (2007). Advanced Mathematicsand Science Coursetaking in the Spring High School Senior Classes of 1982, 1992, and2004 (NCSE 2007-312). Washington, DC :National Center for Education Statistics,Institute of Education Sciences, U.S. Department of Education.

Detracking 37DiPrete, Thomas A., Eirich, Gregory M. (2006). Cumulative Advantage as a Mechanism forInequality: A Review of Theoretical and Empirical Developments. Annual Review ofSociology, 32, 271-297.Duncan, O.D. and Duncan, B. (1955). A methodological analysis of segregation indexes.American Sociological Review, 20, 210-217.Farkas, George. Cognitive Skills and Noncognitive Traits and Behaviors in StratificationProcesses. Annual Review of Sociology, 29, 541-563.Gamoran, Adam and Eileen C. Hannigan. (2000). Algebra for Everyone? Benefits of College-Preparatory Mathematics for Students With Diverse Abilities in Early Secondary School.Educational Evaluation and Policy Analysis, 22, 241-254.Gamoran, Adam, Martin Nystrand, Mark Berends, and Paul C. LePore. (1995). AnOrganizational Analysis of the Effects of Ability Grouping. American EducationalResearch Journal, 32, 687-715Gamoran, Adam. (1996). Curriculum Standardization and Equality of Opportunity in ScottishEducation: 1984-90. Sociology of Education, 69, 1-21.Gamoran, A. Weinstein, M. (1998). Differentiation and Opportunity, in Restructured Schools.American Journal of Education, 106, 385-415.Hallinan, Maureen T. 1994. Tracking: From Theory to Practice. Sociology of Education. 67, 79-84.Kelly, Sean. (2007). The Contours of Tracking in North Carolina. The High School Journal, 90,15-31.Kelly, Sean. (2009). The Black-White Gap in Mathematics Course Taking. Sociology ofEducation, 82, 47-69.Koenker, Roger, and Kevin F. Hallock. (2001). Quantile Regression. Journal of EconomicPerspectives 15:143–56.Lee, V.E. (1993). Educational Choice: The Stratifying Effects of Selecting Schools and Courses.Educational Policy 7:125-148.Lee, V.E., Croninger, R.G., & Smith, J.B., (1997). Course-taking, equity, and mathematicslearning: Testing the constrained curriculum hypothesis in U.S. secondary schools.Education Evaluation and Policy Analysis, 19(2), 99-121.Lee, V.E. and Smith, J.B. (1995). Effects of High School Restructuring and Size on Gains inAchievement and Engagement for Early Secondary School Students. Sociology ofEducation, 68 (4), 241-270.

Detracking 38Loveless, T. (1999). The tracking wars: State reform meets school policy. Harrisonburg, VA:R.R. Donnelley and Sons.Lucas, Samuel R. (1999). Tracking inequality: Stratification and mobility in American highschools. New York, NY: Teachers College Press.National Commission on Excellence in Education. (1983). A Nation At Risk.National Governor’s Association. (2005). An Action Agenda for Improving America’s HighSchools. http://www.nga.org/Files/pdf/0502actionagenda.pdfNomi, T. & Allensworth, E. (2009). Double-dose Algebra as an Alternative Strategy toRemediation: Effects on Students’ Academic Outcomes. Journal of Research onEducational Effectiveness. 2: 111-148.Oakes, J. (1985). Keeping Track: How Schools Structure Inequality. New Haven, CT: YaleUniversity Press.Oakes, Jeannie and Gretchen Guiton. (1995). Matchmaking: The Dynamics of High SchoolTracking Decisions. American Educational Research Journal, 32, 3-33.Oakes, J., Wells, A.S., & Jones, M., Datnow, A. (1997). Detracking: The social construction ofability, cultural politics, and resistance to reform. Teachers College Record, 98(3), 482-510.Powell, A.G. and Farrar, E. and Cohen, D.K. (1985.) The Shopping Mall High School. Boston:Houghton Mifflin Boston.Rosenbaum, J.E. (1999). If Tracking Is Bad, Is Detracking Better? American Educator, 23, 24-29.Rosin, Matthew, Heather Barondess, and Julian Leichty. 2009. “Algebra Policy in California:Great Expectations and Serious Challenges.” EdSource Report.Sandholtz, J.H. and Ogawa, R.T. and Scribner, S.P. (2004). Standards gaps: Unintendedconsequences of local standards-based reform. Teachers College Record, 106, 1177-1202.Sorenson, Aage B. 1970. “Organizational Differentiation of Students and EducationalOpportunity.” Sociology of Education 43: 355-76.Wells, A.S., & Oakes, J. (1996). Potential Pitfalls of Systemic Reform: Early Lessons fromResearch on Detracking. Sociology of Education, 69(Extra Issue), 135-143.Williams, R. (2006). Generalized ordered logit/partial proportional odds models for ordinaldependent variables. Stata Journal, 6, 58-82.

Detracking 39Wilson, B.L., & Rossman, G.B., (1993). Mandating academic excellence: High school responsesto state curriculum reform. New York, NY: Teachers College PressYonezawa, S., Wells, A.S., & Sarna, I. (2002). Choosing Tracks:“Freedom of Choice” inDetracking Schools. American Educational Research Journal, 39(1), 37-67.Zimmer, Ron. (2003). A new twist in the educational tracking debate. Economics of EducationReview, 22: 307-315.

Detracking 40Table 1: Descriptive statistics by cohort2004-20052005-20062006-20072007-2008Gen Math in 8th grade (n) 2,433 1,931 1,022 648(%) 64.18 51.36 25.58 16.1Algebra in 8th grade (n) 1,216 1,520 2,512 2,848(%) 32.08 40.43 62.86 70.76Geometry in 8th grade (n) 142 309 462 529(%) 3.75 8.22 11.56 13.14ELL in 8th grade (n) 1,482 1,344 1,336 1,378(%) 39.08 35.74 33.3 34.2RFEP in 8th grade (n) 884 993 1,181 1,226(%) 23.31 26.41 29.44 30.43Eng only/FEP in 8th grade (n) 1,426 1,423 1,495 1,425(%) 37.61 37.85 37.26 35.37Hispanic (n) 1,955 1,905 2,144 2,178(%) 51.56 50.66 53.44 54.06Vietnamese (n) 835 875 948 978(%) 22.02 23.27 23.63 24.27White (n) 693 642 599 532(%) 18.28 17.07 14.93 13.2Other (n) 309 338 321 341(%) 8.15 8.99 8 8.467th grade math score -0.098 0.030 0.064 -0.017th grade ELA score -0.146 -0.021 0.053 0.103Note: 7th grade math and ELA scores are standardized across cohorts.

Detracking 41Table 2: 8 th grade math course enrollment odds, generalized ordered logistic regression.(Standard errors in parentheses)Model 1 Model 2 Model 3>=Algebra Geometry >=Algebra Geometry >=Algebra Geometry(2004-2005)2005-2006 1.772** 1.772** 2.098*** 2.098*** 2.232*** 2.232***(0.333) (0.333) (0.366) (0.366) (0.452) (0.452)2006-2007 5.283*** 2.817*** 15.184*** 3.458*** 12.679*** 12.679***(1.148) (0.854) (4.202) (1.116) (2.757) (2.757)2007-2008 9.671*** 3.306*** 43.305*** 4.657*** 22.384*** 22.384***(2.146) (1.029) (12.172) (1.538) (4.708) (4.708)Hispanic 1.261 1.261 1.272 1.272(0.191) (0.191) (0.190) (0.190)Vietnamese 1.599* 3.108*** 1.556* 3.135***(0.324) (0.577) (0.314) (0.581)Other 1.506* 2.736*** 1.494* 2.846***(0.249) (0.398) (0.250) (0.421)ELL 1.239* 0.465*** 1.259* 0.439***(0.117) (0.103) (0.118) (0.099)Reclassified English 1.451*** 1.451*** 1.436*** 1.436***(0.098) (0.098) (0.095) (0.095)7 th grade Math (std) 8.547*** 2.611*** 11.746*** 4.779***(0.734) (0.293) (1.857) (1.011)7 th grade ELA (std) 1.589*** 3.679*** 1.965*** 4.537***(0.095) (0.338) (0.184) (0.580)7 th Gr Math * 2006 1.366 1.366(0.316) (0.316)7 th Gr ELA * 2006 0.813 0.813(0.110) (0.110)7 th Gr Math * 2007 0.625* 0.625*(0.136) (0.136)7 th Gr ELA * 2007 0.626*** 0.626***(0.084) (0.084)7 th Gr Math * 2008 0.311*** 0.311***(0.059) (0.059)7 th Gr ELA * 2008 0.907 0.907(0.119) (0.119)Constant 0.556*** 0.047*** 0.367*** 0.005*** 0.356*** 0.001***(0.085) (0.012) (0.078 (0.001 (0.083) (0.000)N 15,233 13,734 13,734* p

Detracking 1Table 3: 10 th grade math course enrollment odds, generalized ordered logistic regression. (Standard errors inparentheses)Model 1: Model 2: Model 3:Geometry Alg II Summ. Geometry Alg II Summ. Geometry Alg II Summ.2004-2005 -- -- -- -- -- -- -- -- ---- -- -- -- -- -- -- -- --2005-2006 1.664*** 1.196 1.433 2.063*** 1.179 1.423 1.711*** 1.152 1.019(0.226) (0.204) (0.373) (0.238) (0.185) (0.353) (0.212 (0.198) (0.275)2006-2007 3.035*** 1.578** 1.515 4.686*** 2.017*** 1.485 3.744*** 2.206*** 1.469(0.4) (0.264) (0.454) (0.539) (0.306) (0.450) (0.497 (0.352) (0.463)2007-2008 4.464*** 1.497* 1.831* 7.066*** 1.750*** 2.054* 6.602*** 1.890*** 2.484**(0.66) (0.251) (0.525) (0.852) (0.272) (0.590) (1.054 (0.314) (0.776)Hispanic 1.048 1.048 1.048 1.03 1.03 1.03(0.090) (0.090) (0.090) (0.088 (0.088) (0.088)Vietnamese 3.208*** 3.208*** 3.208*** 3.141*** 3.141*** 3.141***(0.334) (0.334) (0.334) (0.326 (0.326) (0.326)Other 1.577*** 2.247*** 2.952*** 1.571** 2.211*** 2.980***(0.215) (0.267) (0.371) (0.218 (0.266) (0.383)ELL 1.112 1.112 1.112 1.113 1.113 1.113(0.076) (0.076) (0.076) (0.076 (0.076) (0.076)Reclassified English 1.121 1.428*** 1.664*** 1.114 1.439*** 1.628***(0.106) (0.109) (0.155) (0.105 (0.109) (0.150)7 th grade Math (std) 4.835*** 7.422*** 3.108*** 5.771*** 11.322*** 5.947***(0.344) (0.537) (0.304) (0.613 (1.405) (0.872)7 th grade ELA (std) 1.449*** 1.843*** 3.279*** 1.659*** 1.659*** 1.659***(0.09) (0.107) (0.276) (0.126 (0.126) (0.126)7 th Gr Math * 2006 0.911 0.911 0.911(0.116 (0.116) (0.116)7 th Gr ELA * 2006 0.694** 0.978 1.640*(0.091 (0.119) (0.327)7 th Gr Math * 2007 0.630*** 0.630*** 0.630***(0.084 (0.084) (0.084)7 th Gr ELA * 2007 1.027 0.889 1.769***(0.153 (0.098) (0.291)7 th Gr Math * 2008 0.806 0.403*** 0.294***(0.168 (0.064) (0.048)7 th Gr ELA * 2008 0.958 1.486** 2.779***(0.143 (0.190) (0.377)Constant 2.413*** 0.615*** 0.094*** 2.801*** 0.231*** 0.009*** 3.184*** 0.218*** 0.008***(0.242) (0.086) (0.018) (0.276) (0.035) (0.001) (0.323) (0.035) (0.001)N 11,920 11005 11005* p

Detracking 1Table 4: Segregation in 8 th grade mathematics classrooms, 2004-2005 to 2007-2008 (index of dissimilarity)Gender2004-2005 2005-2006 2006-2007 2007-2008Male/Female 0.25 0.21 0.23 0.24EthnicityHispanic/VietnameseHispanic/non-HispanicLanguage StatusELL/Fluent English7 th Grade Mathematics Test ScoreTop 25%/Bottom 25%Top 50%/Bottom 50%7 th Grade ELA Test ScoreTop 25%/Bottom 25%Top 50%/Bottom 50%N(Classrooms)0.58 0.57 0.55 0.580.48 0.48 0.48 0.510.46 0.45 0.48 0.450.92 0.93 0.81 0.790.68 0.71 0.59 0.520.81 0.78 0.74 0.770.57 0.55 0.51 0.52256 204 213 241

Detracking 2Table 5: Peer quality and skill heterogeneity 8 th grade math classrooms2004-2005 2005-2006 2006-2007 2007-2008Peer quality (Classroom mean, 7 th grade math percentile)General Math 32.14 30.29 23.84 19.66Algebra 72.20 69.35 57.31 51.87Geometry 93.09 88.52 87.76 77.76All courses 46.90 50.63 52.18 50.58Low-performing peers (% of classroom below basic on 7 th grade math)General Math 42.11 45.35 55.48 67.38Algebra 0.87 1.55 11.34 15.28Geometry 0.00 0.00 0.00 1.15All courses 26.39 22.39 20.27 20.67Skill heterogeneity (Classroom IQR, 7 th grade math percentile)General Math 22.68 23.76 18.20 18.68Algebra 23.45 24.01 31.02 29.54Geometry 7.15 14.12 13.26 25.5All courses 22.36 23.05 25.79 27.37

Detracking 3Table 6: OLS regression coefficients, 10 th grade math test scoresModel 1 Model 2 Model 3 Model 4 Model 5 Model 62004-20052005-2006 0.084 -0.044* -0.073* -0.077** -0.063* -0.056*(0.073) (0.019) (0.028) (0.027) (0.025) (0.025)2006-2007 -0.012 -0.128*** -0.143*** -0.126*** -0.096** -0.085*(0.071) (0.019) (0.033) (0.032) (0.031) (0.034)2007-2008 0.01 -0.084*** -0.227*** -0.212*** -0.153*** -0.117**(0.073) (0.02) (0.041) (0.039) (0.037) (0.038)Hispanic -0.139*** -0.144*** -0.149*** -0.115*** -0.125***(0.021) (0.019) (0.019) (0.019) (0.019)Vietnamese 0.236*** 0.211*** 0.207*** 0.212*** 0.212***(0.024) (0.022) (0.023) (0.022) (0.022)Other 0.096*** 0.073** 0.071** 0.072** 0.081***(0.023) (0.023) (0.023) (0.023) (0.023)ELL -0.011 -0.013 -0.012 -0.006 -0.006(0.017) (0.016) (0.016) (0.016) (0.016Reclassified English 0.063*** 0.045** 0.042** 0.047*** 0.042**(0.015) (0.014) (0.015) (0.014) (0.014)7 th grade Math (std) 0.589*** 0.537*** 0.534*** 0.480*** 0.494***(0.016) (0.017) (0.017) (0.017) (0.017)7 th grade ELA (std) 0.191*** 0.156*** 0.152*** 0.139*** 0.136***(0.012) (0.011) (0.011) (0.011) (0.011)8 th grade Algebra 0.326*** 0.331*** 0.118*** 0.214***(0.032) (0.032) (0.033) (0.027)8 th grade Geometry 0.080 0.159** -0.315*** 0.028(0.054) (0.054) (0.065) (0.049)Algebra * 2006 -0.015 -0.014 -0.008 -0.042(0.038) (0.038) (0.035) (0.035)Algebra * 2007 -0.149*** -0.200*** -0.117** -0.192***(0.039) (0.041) (0.037) (0.039)Algebra * 2008 -0.067 -0.111* -0.041 -0.154***(0.046) (0.045) (0.042) (0.042)Geometry * 2006 0.179** 0.154** 0.212** 0.163**(0.054) (0.055) (0.069) (0.051)Geometry * 2007 0.238*** 0.195** 0.258*** 0.160**(0.062) (0.062) (0.071) (0.060)Geometry * 2008 0.532*** 0.439*** 0.605*** 0.388***(0.061) (0.06) (0.067) (0.057)Math course skill heterogeneity (IQR) 0.004***(0.001)Math course peer quality (mean) 0.242***(0.021)% math course peers below basic -0.514***(0.048)Constant 0.012 0.011 -0.099*** -0.091*** -0.022 0.057*-0.056 -0.023 -0.024 -0.024 (0.022) (0.026)N 11,961 11,278 11,278 11,278 11,278 11,278* p

Detracking 4Figure 1: Quantile regression estimates of the effects of curricular intensification across the 10 th grade math testscore distribution